Speaking after the court ruling on Thursday, Romney said: "Obamacare was bad policy yesterday, it's bad policy today." He said he would seek to repeal it on his first day in office, should he be elected.
Romney's former rival for the Republican nomination, Michele Bachmann, also weighed in, describing the justices as an "activist court". House speaker John Boehner saying the ruling "underscores the urgency of repealing" the bill.
In a prepared statement delivered to TV cameras with the Capitol in the background, Romney said: "As you might imagine, I disagree with the supreme court's decision, and I agree with the dissent.
"What the court did not do on its last day in session, I will do on my first day if elected president of the United States, and that is I will act to repeal Obamacare.
"What the court did today is say that Obamacare does not violate the constitution. What they did not do was say that Obamacare is good law, or that it's good policy.
"Obamacare was bad policy yesterday, it's bad policy today. Obamacare was bad law yesterday, it's bad law today."
Obama's healthcare bill is widely accepted to been influenced by Romney's own healthcare legislation introduced when he was governor of Massachusetts. Prior to introducing the bill in March 2010, Obama and senior White House officials had a dozen meetings with consultants who shaped the legislation.
But despite the political obstacles in doing so, Romney made it clear he would make healthcare a central part of his campaign. "This is a time of choice for the American people," Romney said. "Our mission is clear. If we want to get rid of Obamacare, we're going to have to replace President Obama. My mission is to make sure we do exactly that."
Romney's one-time presidential rival Michelle Bachmann was quick to add her voice to the opposition on Thursday, saying she was "deeply disappointed" by the supreme court ruling.
"We're profoundly disappointed in the decision from the court," Bachmann told CNN from outside the supreme court. "But I urge people to read the dissent … because that opinion said very clearly, this was an activist court that you saw today."
In a statement, she added: "Obamacare represents the largest expansion of entitlement spending and a playground of left-wing social engineering in our country's history, and must be stopped," Bachmann said in a statement, adding that the bill should be repealed.
"Obamacare is socialized medicine that threatens the quality of our healthcare and worse, the foundations of our republic."
Boehner said Republicans "stand ready to work with a president who will listen to the people and will not repeat the mistakes that gave our country ObamaCare", but did not mention Romney by name.
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